{"id":6066,"date":"2023-04-08T18:53:34","date_gmt":"2023-04-09T01:53:34","guid":{"rendered":"http:\/\/theoryofeverything.org\/theToE\/?p=6066"},"modified":"2023-10-07T06:34:21","modified_gmt":"2023-10-07T13:34:21","slug":"comparing-two-different-5-cell-cartesian-coordinate-sets","status":"publish","type":"post","link":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/","title":{"rendered":"Comparing two different 5-Cell  Cartesian Coordinate sets"},"content":{"rendered":"\n<p>This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell <a href=\"https:\/\/en.wikipedia.org\/wiki\/Talk:5-cell#Coordinates\" target=\"_blank\" rel=\"noopener\" title=\"\">here<\/a>.  I created a visualization of the these. Click <a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Comparing hyperpyramid to translated simplest 5-cell.nb\" target=\"_blank\" rel=\"noopener\" title=\"\">here<\/a> for the Mathematica Notebook or see the image below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Comparing hyperpyramid to translated simplest 5-cell.svg\" target=\"_blank\" rel=\"noreferrer noopener\"><img decoding=\"async\" src=\"https:\/\/theoryofeverything.org\/TOE\/JGM\/Comparing hyperpyramid to translated simplest 5-cell.svg\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<p>Greg Moxness<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[8,13,14],"class_list":["post-6066","post","type-post","status-publish","format-standard","hentry","category-physics","tag-3d","tag-4d","tag-math"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"jgmoxness\"\/>\n\t<link rel=\"canonical\" href=\"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!\" \/>\n\t\t<meta property=\"og:description\" content=\"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness\" \/>\n\t\t<meta property=\"og:url\" content=\"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2023-04-09T01:53:34+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2023-10-07T13:34:21+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!\" \/>\n\t\t<meta name=\"twitter:description\" content=\"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#blogposting\",\"name\":\"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!\",\"headline\":\"Comparing two different 5-Cell  Cartesian Coordinate sets\",\"author\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"publisher\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/theoryofeverything.org\\\/TOE\\\/JGM\\\/Comparing hyperpyramid to translated simplest 5-cell.svg\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#articleImage\"},\"datePublished\":\"2023-04-08T18:53:34-07:00\",\"dateModified\":\"2023-10-07T06:34:21-07:00\",\"inLanguage\":\"en-US\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#webpage\"},\"isPartOf\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#webpage\"},\"articleSection\":\"Physics, 3D, 4D, Math\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}},{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"position\":2,\"name\":\"Physics\",\"item\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#listItem\",\"name\":\"Comparing two different 5-Cell  Cartesian Coordinate sets\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE#listItem\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#listItem\",\"position\":3,\"name\":\"Comparing two different 5-Cell  Cartesian Coordinate sets\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/topics\\\/physics\\\/#listItem\",\"name\":\"Physics\"}}]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\",\"name\":\"jgmoxness\"},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\",\"url\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/\",\"name\":\"jgmoxness\"},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#webpage\",\"url\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/\",\"name\":\"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!\",\"description\":\"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness\",\"inLanguage\":\"en-US\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#website\"},\"breadcrumb\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/2023\\\/04\\\/08\\\/comparing-two-different-5-cell-cartesian-coordinate-sets\\\/#breadcrumblist\"},\"author\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"creator\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/author\\\/jgmoxness\\\/#author\"},\"datePublished\":\"2023-04-08T18:53:34-07:00\",\"dateModified\":\"2023-10-07T06:34:21-07:00\"},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#website\",\"url\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/\",\"name\":\"Visualizing a Theory of Everything!\",\"description\":\"Dedicated to the pursuit of beauty and Truth in Nature!\",\"inLanguage\":\"en-US\",\"publisher\":{\"@id\":\"http:\\\/\\\/theoryofeverything.org\\\/theToE\\\/#person\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!","description":"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness","canonical_url":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BlogPosting","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#blogposting","name":"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!","headline":"Comparing two different 5-Cell  Cartesian Coordinate sets","author":{"@id":"http:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"publisher":{"@id":"http:\/\/theoryofeverything.org\/theToE\/#person"},"image":{"@type":"ImageObject","url":"https:\/\/theoryofeverything.org\/TOE\/JGM\/Comparing hyperpyramid to translated simplest 5-cell.svg","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#articleImage"},"datePublished":"2023-04-08T18:53:34-07:00","dateModified":"2023-10-07T06:34:21-07:00","inLanguage":"en-US","mainEntityOfPage":{"@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#webpage"},"isPartOf":{"@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#webpage"},"articleSection":"Physics, 3D, 4D, Math"},{"@type":"BreadcrumbList","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE#listItem","position":1,"name":"Home","item":"http:\/\/theoryofeverything.org\/theToE","nextItem":{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","name":"Physics"}},{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","position":2,"name":"Physics","item":"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/","nextItem":{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#listItem","name":"Comparing two different 5-Cell  Cartesian Coordinate sets"},"previousItem":{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE#listItem","name":"Home"}},{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#listItem","position":3,"name":"Comparing two different 5-Cell  Cartesian Coordinate sets","previousItem":{"@type":"ListItem","@id":"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/#listItem","name":"Physics"}}]},{"@type":"Person","@id":"http:\/\/theoryofeverything.org\/theToE\/#person","name":"jgmoxness"},{"@type":"Person","@id":"http:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author","url":"http:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/","name":"jgmoxness"},{"@type":"WebPage","@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#webpage","url":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/","name":"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!","description":"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness","inLanguage":"en-US","isPartOf":{"@id":"http:\/\/theoryofeverything.org\/theToE\/#website"},"breadcrumb":{"@id":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/#breadcrumblist"},"author":{"@id":"http:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"creator":{"@id":"http:\/\/theoryofeverything.org\/theToE\/author\/jgmoxness\/#author"},"datePublished":"2023-04-08T18:53:34-07:00","dateModified":"2023-10-07T06:34:21-07:00"},{"@type":"WebSite","@id":"http:\/\/theoryofeverything.org\/theToE\/#website","url":"http:\/\/theoryofeverything.org\/theToE\/","name":"Visualizing a Theory of Everything!","description":"Dedicated to the pursuit of beauty and Truth in Nature!","inLanguage":"en-US","publisher":{"@id":"http:\/\/theoryofeverything.org\/theToE\/#person"}}]},"og:locale":"en_US","og:site_name":"Visualizing a Theory of Everything! - Dedicated to the pursuit of beauty and Truth in Nature!","og:type":"article","og:title":"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!","og:description":"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness","og:url":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/","article:published_time":"2023-04-09T01:53:34+00:00","article:modified_time":"2023-10-07T13:34:21+00:00","twitter:card":"summary","twitter:title":"Comparing two different 5-Cell Cartesian Coordinate sets - Visualizing a Theory of Everything!","twitter:description":"This is to support an analysis of the 4D polytope called the 5-Cell. For more of the context, there is discussion on the Wikipedia Talk page for the 5-Cell here. I created a visualization of the these. Click here for the Mathematica Notebook or see the image below: Greg Moxness"},"aioseo_meta_data":{"post_id":"6066","title":null,"description":null,"keywords":[],"keyphrases":{"focus":{"keyphrase":"","score":0,"analysis":{"keyphraseInTitle":{"score":0,"maxScore":9,"error":1}}},"additional":[]},"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":"","og_custom_url":null,"og_article_section":null,"og_article_tags":[],"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"BlogPosting","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":"-1","robots_max_videopreview":"-1","robots_max_imagepreview":"large","priority":null,"frequency":"default","local_seo":null,"limit_modified_date":false,"created":"2023-04-09 01:53:19","updated":"2025-06-10 15:54:51"},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"http:\/\/theoryofeverything.org\/theToE\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/\" title=\"Physics\">Physics<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">\u00bb<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tComparing two different 5-Cell  Cartesian Coordinate sets\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"http:\/\/theoryofeverything.org\/theToE"},{"label":"Physics","link":"http:\/\/theoryofeverything.org\/theToE\/topics\/physics\/"},{"label":"Comparing two different 5-Cell  Cartesian Coordinate sets","link":"http:\/\/theoryofeverything.org\/theToE\/2023\/04\/08\/comparing-two-different-5-cell-cartesian-coordinate-sets\/"}],"_links":{"self":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6066","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/comments?post=6066"}],"version-history":[{"count":5,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6066\/revisions"}],"predecessor-version":[{"id":6303,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/posts\/6066\/revisions\/6303"}],"wp:attachment":[{"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/media?parent=6066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/categories?post=6066"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/theoryofeverything.org\/theToE\/wp-json\/wp\/v2\/tags?post=6066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}